GRAPHICAL ALGEBRA. 



71 



Table E shows at once for which values of a we shall get integer values of <p. We 

 can then at once draw the equiscalar curves for integer values of <p in their proper 

 places between the given equiscalar curves for integer values of a. 



As an example we can consider the square of a given field, /(a) = a 2 . Thus 



(c) <p = a* 

 Solving with respect to a we get 



(d) a = Vtp 



a is tabulated for integer values of <p in table F. 



Table F. Square-root table for passing from the field of a scalar to the field of its square. 



This table shows that the curve <p = 50 coincides with the curve a = 7.1, curve 

 <p = 60 with curve a = 7.7, and so on. Fig. 64 shows how by use of this information 



a - 12 tt 



<X=i 



Fig. 64. Field of a given scalar (fine lines = 7,8,9, 

 . . . ) and field of its square (thick lines <f = 50, 60, 

 70, . . .) 



Fig. 65. Field of an angle (fine lines a=o, 4, 8, 12, 

 . . . ) and field of its cosine (thick lines (f = 1 .0, 

 0.9,0.8 . . .) 



the curves for integer values of <p are drawn in their proper places between the curves 

 for integer values of a. For evident reasons we have drawn the curves <p = const, 

 for ten times greater intervals than the curves a = const. 



To use another example, let the field of a multiple-valued scalar, the angle a, be 

 given, expressed by the numbers 0-63. It is required to find the field of the scalar 



(e) <p = cos a 



